Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high.

To make Saffron Spread, heat a non-stick, fire-proof skillet with olive oil over grill. Add shallots, garlic, saffron threads and wine. Heat, stirring occasionally. Cook until mixture is reduced and thickened, about 10 minutes. Transfer to a small bowl and let cool. Once cooled, add mayonnaise and mix well. Cover and refrigerate until ready to use.

To make carmelized onion topping, heat non-stick fire-proof skillet with olive oil over grill. Add onions, garlic, brown sugar, vinegar, salt and pepper. Cook covered until onions are soft. Add wine and continue to cook covered over grill until wine is reduced. Remove from grill and set aside until ready to use.
To make the patties, in a large bowl, combine the meat, chorizo, capers, onion, egg, bread crumbs, salt and pepper. Ensure the ingredients are well distributed throughout the meat. Add the sliced olives, handling the meat as little as possible to avoid compacting it. Divide the meat into 6 equal portions to fit size of rolls. Place patties onto a platter, cover with plastic wrap and refrigerate until ready to grill.

When the grill is ready, brush the grill rack with vegetable oil. Place the patties on the rack, cover and cook, turning once until done to preference, 5 – 7 minutes on each side for medium. While grilling, lightly baste patties on both sides with a mist of red wine from the spray bottle. Meanwhile, place the skillet with the caramelized onions on the side of the grill to keep warm until patties are done. Place the cheese slices on the patties during the last 2 or 3 minutes of grilling and place the buns cut side down on the outer edges of the rack to toast lightly.

To assemble the burgers, spread a generous amount of saffron spread over the cut side of the rolls. On each roll bottom, place a patty, an equal portion of the carmelized onion topping, and a lettuce leaf. Add the roll tops and serve.